I don't tie a ton of emergers, but when I do I leave them unweighted so they sit a bit higher in the water, like they're coming up to the surface. I'm sure you could do it either way depending on what you're after though

I struggle with fishing the right depth so I tend to tie emergers both ways, with and without bead. The only emerger I tie exclusively with a bead is a BWO Barr Emerger, dont know why but a beadhead barr emerger is one of my "confidence patterns"

I don't put weight on them. As mentioned, it lets them move more freely, like they might be rising (emerging). Also it gives flexibility. Sometimes I fish them in the surface film/near the surface, other times I put a bit of weight 12 - 18 inches above them on the tippet. This lets them float a bit off the bottom.